# Inequalities for some integrals involving modified Lommel functions of the first kind

## TL;DR

This paper derives tight inequalities for integrals involving the modified Lommel function of the first kind, generalizing recent bounds for related special functions and providing new bounds for hypergeometric functions.

## Contribution

It introduces new tight inequalities for integrals of the modified Lommel function, extending previous bounds for the modified Struve function and relating to hypergeometric functions.

## Key findings

- Derived tight inequalities for integrals involving the modified Lommel function.
- Generalized recent bounds for integrals of the modified Struve function.
- Established a tight double inequality for a hypergeometric function.

## Abstract

In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the modified Lommel function $t_{\mu,\nu}(x)$, for a generalized hypergeometric function. The inequalities obtained in this paper generalise recent bounds for integrals involving the modified Struve function of the first kind.